He won the 2004 Aa St Omer Open to gain a place on the European Tour.

His father worked at Saint-Nom-La-Bretèche, which was the host course of the Trophée Lancôme until that tournament ceased in 2003, and was his son's first coach.

Lima was the top ranked French amateur at the end of 2001 and turned professional the following year.

After an unsuccessful 2015 on the Challenge Tour, Lima won the 2016 Najeti Open and was runner-up in the Ras Al Khaimah Golf Challenge to finish 12th in the Order or Merit and gain promotion to the European Tour for the fourth time.

After a poor start to 2019, Lima was joint runner-up in the Euram Bank Open behind Calum Hill in July and won the Vierumäki Finnish Challenge two weeks later.